Thursday, August 19, 2010

Mathematics and computer science

I haven't written much lately since we have been travelling. Now I am working on a paper and I am faced once more with the difficulties of working between two fields with different cultures, mathematics and computer science. As I have mentioned elsewhere I worked as a mathematician for 20+ years and then as a computer scientist for 20 years. Perhaps it would be more accurate to say as a mathematician working on computer science for the last 20 years, since the first years have a more profound effect. However my direction really changed around 1990 and I see mathematics differently now.

I want to make a series of observations about this experience as they occur to me, not in any particular order. I will collect them all in this post even though I write them over time.

1. The debate over Tuesdays child which as far as I am concerned was never resolved (even in Peter Cameron's blog) illustrates one hugely important fact about mathematics. It seems to be the only subject where arguments can be clearly decided and resolved. Its is also the limitation of mathematics - we do want to understand the world and that is outside such certainty.

2. Computer scientists, even theoreticians, are very rough in creating models. At least to my taste. They are influenced by engineers for whom what works, as soon as possible, in OK. But this to me is no way to create theories. I believe from my mathematical experience that there is usually a correct way to do things, which needs to be distilled from experience.

3. Let's look at the success of Google. A mathematician looking at this imagines that the important thing was the algorithm for rating web pages, and take credit for the fact that this comes from the theory of Markov chains (just as physicists take credit for the world wide web because it was developed at CERN; one would hope something useful came out of all that expense). The algorithm is clearly important but if you look at the first paper by Brin and Page (which I see now was presented in Brisbane!) it is much more about the architecture of Google and the problem of implementing search as rapidly as possible using a large number of machines. The algorithm is a very small part of the achievement.

4. To be continued.

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